Reasoning about Priority Relations

Abstract

Whereas in Chapter 6 arguments could only be compared with respect to specificity, in Chapter 7 any criterion has been allowed, provided that it can be expressed as an ordering on rules. However, apart from specificity almost nothing has yet been said about the possible sources of the priorities. For some time in AI the (often implicit) hope has been that the sources of these priorities are of a general, domain independent nature. As a consequence, the question where these priorities can be found is usually not treated as a matter of common-sense reasoning. If this question is addressed at all, then it is usually considered a metalogical issue. In particular, much research has concentrated on formalising the specificity principle, which, as we have seen, can be expressed in purely logical terms. However, a brief look at the legal domain already suffices to see that the hope that we can find useful domain-independent sources of preferences is unrealistic. In law, but also in many other domains of common-sense reasoning, such as bureaucracies, collision rules are themselves part of the domain theory (see e.g. the detailed overview of Peczenik, 1990 in the context of Swedish law). This even holds for specificity; although checking which argument is more specific may be a logical matter, deciding to prefer the most specific argument is a legal decision. Moreover, the collision rules not only vary from domain to domain, they can also be incomplete or inconsistent, in the same way as ‘ordinary’ domain information can be. In other words, reasoning about priorities is nonmonotonic reasoning. These observations mean that in a logic that is meant to formalise this kind of reasoning, the consequences of a set of premises do not only depend on the priorities, they also determine the priorities. In most current nonmonotonic logics these observations are ignored (but see Chapter 9 for some exceptions).